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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 84
PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 86
Incomplete Factorization for Preconditioning Shifted Linear Systems H. Sarmiento, A. Suárez and G. Montero
University Institute of Intelligent Systems and Numerical Applications in Engineering (IUSIANI), University of Las Palmas de Gran Canaria, Spain Full Bibliographic Reference for this paper
, "Incomplete Factorization for Preconditioning Shifted Linear Systems", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Fifth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 86, 2006. doi:10.4203/ccp.84.86
Keywords: incomplete Cholesky factorization, shifted linear systems, preconditioning, conjugate gradient, iterative methods, wind modelling.
Summary
The resolution of several problems of science and engineering, such as parabolic partial differential equations, mass consistent models for wind field adjustment [1,2], with any discretization technique, yields linear systems of equations of the form,
where M and N are constant for a given discretization. In these problems, the system (72) must be solved for different values of ![]() Iterative solvers based on Krylov subspaces are the most efficient methods for such large and sparse linear systems [3]. In our case, since M and N are symmetric positive definite matrices, the Conjugate Gradient (CG) provides the best results. In addition, the use of suitable preconditioning techniques [4] allows a faster convergence of the CG.
For preconditioning these systems, we can build a different preconditioner for each value of
In this work, an intermediate procedure is proposed. It consists of a preconditioner based on an incomplete Cholesky factorization that may be updated for each new system at a low computational cost. Thus, it provides better convergence than the latter strategy and is cheaper that the former. In a similar way, Meurant [5] proposes this preconditioner for the special case
Several numerical experiments are presented in order to show the efficiency of the proposed preconditioner. References
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